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It was recently demonstrated by Malestein, Rivin, and Theran that the cardinality of such a collection is no more than $2g+1$. In this paper, we show that for $g\\geq 3$, there exists at least two such collections with this maximum size up to the action of the mapping class group, answering a question posed by Malestein, Rivin and Theran."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.2797","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-10T04:15:56Z","cross_cats_sorted":[],"title_canon_sha256":"606ea810ac170e780a699aa96cd3b54b6332d5ceed691505abb63ed4b80bb773","abstract_canon_sha256":"f03f4199b515c759c0a17a381606ba1d6b31c270a251114dd92f69984741f927"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:31.505958Z","signature_b64":"AXt/hKALCG/Ou1uRGBMH65IsU1E7qgeF6xqVw9pQeVhKNxA4slsQQsrCWeCrw6bPPvUN1mQpiSo+Xpdp1aBsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ad90e31ca740185f6263a30cde1c9d98af4a736d4943929eef23443bfc92265","last_reissued_at":"2026-05-18T03:43:31.505239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:31.505239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large Collections of Curves Pairwise Intersecting Exactly Once","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Tarik Aougab","submitted_at":"2012-10-10T04:15:56Z","abstract_excerpt":"Let $\\Omega=(\\omega_{j})_{j\\in I}$ be a collection of pairwise non-isotopic simple closed curves on the closed, orientable, genus $g$ surface $S_{g}$, such that $\\omega_{i}$ and $\\omega_{j}$ intersect exactly once for $i\\neq j$. 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